Guys - i can't believe it. I finally got it working...

Thanks to @cuttoon for giving me the cruicial hint. In fact, the pinout i used was wrong. After some more tries i finally got it working:

I used Pin 5, 4 and 3 of the DB9 and had to switch pin 5 and 4 on the side of the din plug. To tell you the truth - i still don't quite understand it completely and i'm not sure if this drawing of the pinout ist correct now (since i'm using not a female din connector but rather a male plug). But that's totally ok, since i'm also lacking theoretical (and mostly pracitcal) engineering skills. Simply put i just can confirm your statement: Pin counts are a bloody headache! 😁

I know it doesn't sound like much but for me this is the fairytale ending i was hoping for all the time. @cuttoon: If you're ever around in the southern region of our country feel free to pass by to grab your free beer! 😀

PS: Also thanks @vetz for noticing @cuttoon.